1 (a) Betty 计划总共投资 17 美元； 000 共同基金，存款证明，

(b) 使用对偶单纯形法求解以下线性规划问题：

2×2 + x3 15
2×1 x2 + x3 25
x1 0; x2 0; x3 0

1 (a) Betty plans to invest a total of \$17; 000 in mutual funds, certi cates of deposit,
and a high yield savings account. She doesn’t want to invest more in mutual
funds than the sum of her certi cates of deposit and savings because of the risk
involved in mutual funds. She also wants the amount in savings to be at least
half the amount in certi cates of deposit. Her expected returns are 8.5% on the
mutual funds, 5% on the certi cates of deposit, and 3.7% on savings. How much
money should Betty invest in each area in order to have the largest return on her
investments? Formulate this as a linear programming problem, clearly describing
your decision variables, objective function, and constraints. Do not solve the LP
problem. [ 9 marks ]

(b) Solve the following linear programming problem by using the Dual SimplexMethod:
minimise z = 2×1 + 3×2 + 3×3
subject to: x1 2×2  8
2×2 + x3  15
2×1 x2 + x3  25
x1  0; x2  0; x3  0

Clearly provide the optimal solution for the problem and the corresponding ob-
jective function value. [ 8 marks ]